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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Growth and decay of solutions of $y^{(2n)}-py=0$


Author: T. T. Read
Journal: Proc. Amer. Math. Soc. 43 (1974), 127-132
MSC: Primary 34C10
DOI: https://doi.org/10.1090/S0002-9939-1974-0335948-4
MathSciNet review: 0335948
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Abstract: Simple estimates of the rate of growth and decay of certain solutions of ${y^{(2n)}} - py = 0$ on $[0,\infty )$ when $p$ is eventually nonnegative are used to obtain sufficient conditions for the existence of exponential solutions, solutions which approach 0, and ${L^2}(0,\infty )$ solutions.


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Keywords: Exponential growth, monotonic solution, <!– MATH ${L^2}(0,\infty )$ –> <IMG WIDTH="83" HEIGHT="43" ALIGN="MIDDLE" BORDER="0" SRC="images/img1.gif" ALT="${L^2}(0,\infty )$"> solution
Article copyright: © Copyright 1974 American Mathematical Society